Determination of heading from the field measured by magnetic sensors

ABSTRACT

The invention relates to the determination of heading by magnetic sensors, in which a magnetic field is measured by magnetometers and calculation means implement a recursive processing calculating for a given sampling time:
         an estimation of a heading prediction which is a function of the heading determined at the preceding sampling time,   a resetting of the predicted heading thereby estimated as a function of a magnetic heading determined from magnetometer measurements.       

     During said resetting, the calculation means estimate the amplitude of the resetting as a function:
         of a model of the change in magnetic disturbances between two sampling times,   and   of an a priori estimation of the amplitude of the disturbances.

GENERAL TECHNICAL FIELD AND PRIOR ART

The present invention relates, generally speaking, to magneto-inertial techniques.

More precisely, it relates to the determination of heading by magnetometers.

In particular, it advantageously finds application in the case of measurements in urban areas or “indoors”, that is to say inside buildings.

Conventionally, magnetometers are used for the calculation of heading in embedded systems.

In this case, the hypothesis is made that the magnetic field measured by the sensor is the Earth's magnetic field which points, for its horizontal component, to magnetic north. The difference between the direction of magnetic north and geographic north (called magnetic declination) is known and tabulated. Without loss of generality, hereafter it will thus be considered that magnetic north and geographic north are merged, and that the magnetometers thus indicate what will be called north.

Typically, determination methods used for the calculation of heading from magnetometer measurements are based on:

-   -   a modelling which links the measurement supplied by the         magnetometer and information relative to the heading of the         system,     -   a characterisation of the relevance of this relationship for the         measurements made.

In a conventional approach, the calculation implemented may be a Kalman type filtering with the magnetic field as measurement, making it possible to reset the heading that is contained in the state, with a measurement noise that is a function of the characterisation of the relevance.

The modelling consists in writing that the measured magnetic field M contains a heading information, for example by the equation

M=R (ψ,θ,φ)^(T) M _(EARTH)

where R is the rotation matrix making it possible to go from the reference frame of the object to the Earth's inertial reference frame. ψ, θ, φ the Euler angles and M_(EARTH) the Earth's magnetic field.

The relevance of this equation is characterised by a measurement variance, that is to say that it is assumed that the error in this equality is a random Gaussian variable with zero expectation.

This variance serves to calculate automatically the Kalman gain which weights the resetting to take account of different noises (dynamic noises linked to the external environment and magnetometer measurement noises).

In yet another approach, a calculation by linear filtering is implemented using the same type of modelling and characterisation.

In this approach, it is the relative adjustment of the amplitude of the gain of the equation that characterises the relevance thereof. In general, this gain is adjusted by hand. Those skilled in the art will then know how to weight it as a function of the relevance of the modelling.

Thus, in these two approaches, the parameters characterising the relevance of the model (variance in the Gaussian noise in the case of the Kalman filter, gain in the case of linear filtering) are generally constant parameters, independent of the measured magnetic field.

Characterisations of the relevance of the modelling taking into account the measured magnetic field while comparing it to a geomagnetic model of the Earth's magnetic field has recently been proposed, for example in the publications:

-   -   W. T. Faulkner, R. Alwood, W. T. David, and J. Bohlin,         “Gps-denied pedestrian tracking in indoor environments using an         imu and magnetic compass,” in Proceedings of the 2010         International Technical Meeting of The Institute of Navigation,         (San Diego, Calif.), pp. 198-204, January 2010,     -   M. H. Afzal, V. Renaudin, and G. Lachapelle, “Magnetic field         based heading estimation for pedestrian navigation         environments,” in 2011 International Conference on Indoor         Positioning and Indoor Navigation, (Guimaraes, Portugal),         September 2011,

The characterisations thereby carried out do not however give entire satisfaction, firstly because they are based on an a priori model of the magnetic field, which necessitates having a model at least as precise as the desired precision and next, because they do not make it possible to reject all the disturbances.

The document “Unscented Filtering for Spacecraft Attitude Estimation” (J. L. Crassidis and F. Landis Markley) describes a model for estimating the orientation of a spacecraft. This model is based on the application of a Kalman filter and does not take any correlation into account. However this model also has for its part biases that make it not very reliable.

It is also known from the document EP 2 264 485 to propose a simplified model, in which the estimated magnetic field is equal to the sum of the value of the measured magnetic field, plus the value of the magnetic disturbance, plus the value of the measurement noise. However, this model of change in disturbance only takes account of a temporal relationship of the disturbance, which makes it not very reliable.

GENERAL DESCRIPTION OF THE INVENTION

A general aim of the invention is to propose a solution enabling better characterisation of the relevance of the modelling used, notably in highly disturbed environments.

Notably, the invention proposes a method for determining heading by magnetic sensors, in which a magnetic field is measured by magnetometers and calculation means implement a recursive processing calculating for a given sampling time:

-   -   an estimation of a heading prediction which is a function of the         heading determined at the preceding sampling time,     -   a resetting of the predicted heading thereby estimated as a         function of a magnetic heading determined from magnetometer         measurements.

In a preferential embodiment during said resetting, the calculation means estimate the amplitude of the resetting as a function:

-   -   of a model of the change in magnetic disturbances between two         sampling times,     -   and     -   of an a priori estimation of the amplitude of the disturbances.

In this way, the processing takes into account the change in the magnetic heading disturbance between two sampling times and takes account of the potential spatial correlation of the disturbance due to the environment in the case of successive sampling times.

The resetting that results therefrom is more reliable than in the prior art.

Said resetting is advantageously a function of the gradient of the measured magnetic field. In this way, one takes into account the fact that the more the environment is disturbed, the higher the gradient and thus the more the measurement of heading is falsified.

Notably, for a given sampling time k+1, the calculation means estimate a linked heading disturbance by calculating

${\psi^{(d)}\left\lbrack {k + 1} \right\rbrack} = {{{\alpha \lbrack k\rbrack}\left( {{\psi^{(d)}\lbrack k\rbrack} + {\hat{u}\lbrack k\rbrack}} \right)} + {\left( {1 - {\alpha \lbrack k\rbrack}} \right)\frac{\hat{u}\lbrack k\rbrack}{2}} + {v_{\psi^{(d)}}\lbrack k\rbrack}}$ where ${\alpha \lbrack k\rbrack} = {1 - \frac{{\sigma_{u}\lbrack k\rbrack}^{2}}{2{a\lbrack k\rbrack}^{2}}}$

and v_(ψ(d)) is a random Gaussian variable of variance

a[k]²(1−α[k]²)

-   -   k being the preceding sampling time,     -   a[k] being a parameter which represents the a priori amplitude         of the magnetic disturbance,     -   û and σ_(u) being two parameters calculated by the calculation         means as an estimation of the expectation and the variance in         the change in the disturbance.

Advantageously, the calculation means estimate the parameter a[k] as a linear function of the norm of the magnetic field gradient.

The parameter û[k] is for its part for example calculated by the calculation means as the difference between the magnetic headings determined directly from magnetometer outputs for the times k+1 and k, from which is subtracted the change in predicted heading (ω[k]dt).

The parameter σ_(u) may be estimated as a function of the velocity of displacement or the displacement between two successive sampling times.

The processing implements for example a Kalman filtering of which the state has at least as parameter the real heading and the magnetic heading disturbance (ψ, ψ^((d))).

The heading prediction may be determined as a function of measurements of one or more sensors of an inertial unit.

The change model is determined beforehand to take account of a spatial or temporal correlation of the changes in disturbances.

The invention further relates to a device for determining heading by magnetic sensors, comprising magnetometers and calculation means for the calculation of the heading from the magnetic field measured by said magnetometers, characterised in that the calculation means implement, for different successive sampling times, the aforesaid processing.

It also proposes a magneto-inertial navigation system comprising at least one such heading measurement device.

Such a system is advantageously used in urban environments or inside buildings.

The invention also relates to:

-   -   a computer programme product including code instructions for the         execution of a method of the aforesaid type, when said programme         is executed on a computer;     -   A storage means readable by a computer equipment on which a         computer programme product includes code instructions for the         execution of such a method.

DESCRIPTION OF THE FIGURES

Other characteristics and advantages of the invention will become clearer from the description that follows, which is purely illustrative and non-limiting, and which should be read with regard to the appended figures in which:

FIG. 1 is a diagram of equipment for the implementation of the method according to the invention;

FIG. 2 represents in greater detail an example of case for the implementation of the method according to the invention;

FIG. 3 illustrates the main steps of a method complying with an embodiment of the invention.

DESCRIPTION OF ONE OR MORE EMBODIMENTS General Remarks—Measurement Device

With reference to FIG. 1, the proposed measurement device is for example used for the estimation of the movement of an object 1 moving in an ambient magnetic field (typically the Earth's magnetic field, which could be slightly altered by nearby metal objects), noted {right arrow over (B)}. As is known, the magnetic field is a three-dimensional vector field, that is to say associating a vector of three dimensions with each three-dimensional point in which the object is moveable.

This object 1 may be any moveable object of which knowledge of the position is desired, for example a wheeled vehicle, a drone, etc., but also a pedestrian.

The object 1 comprises in a case 2 (support) a plurality of magnetic measurement sensors 20, i.e. axial magnetometers 20. Axial magnetometer is taken to mean an element capable of measuring a component of said magnetic field, i.e. the projection of said magnetic field vector {right arrow over (B)} at the level of said magnetometer 20 along its axis.

More precisely, the magnetometers 20 are integral with the case 2. They have a movement substantially identical to the case 2 and to the object 1 in the terrestrial reference frame.

Preferably, the reference frame of the object 1 is provided with an orthonormal cartesian point of reference in which the magnetometers 20 have a predetermined position in this point of reference.

In FIG. 2, the case 2 is fixed onto the object 1 (for example a limb of the pedestrian) by attachment means 23. These attachment means 23 consist for example of a bracelet, for example a self-gripping strap that grips the limb and enables an integral link.

Obviously, the invention is not limited to the estimation of the movement of a pedestrian, but it is particularly advantageous in such a use because it enables very reduced bulk, which is necessary for the case to be portable by a human in an ergonomic manner.

The case 2 may include calculation means 21 (typically a processor) for implementing directly in real time the processing operations of the present method, or instead the measurements may be transmitted via communication means 25 to an external device such as a mobile terminal (smartphone) 3, or even a remote server 4, or instead the measurements may be recorded in local data storage memory means 22 (a flash type memory for example) for a posteriori processing for example on the server 4.

The communication means 25 may implement a short range wireless communication, for example Bluetooth or Wi-Fi (in particular in an embodiment with a mobile terminal 3) or even be means for connecting to a mobile network (typically UMTS/LTE) for a long distance communication. It should be noted that the communication means 25 may be for example a wired connection (typically USB) for transferring data from the local data storage means 22 to those of a mobile terminal 3 or a server 4.

If it is a mobile terminal 3 (respectively a server 4) that hosts the “intelligence”, it includes calculation means 31 (respectively 41) such as a processor for implementing the processing operations of the present method that are going to be described. When the calculation means used are those 21 of the case 2, it may further include communication means 25 for transmitting the estimated position. For example the position of the bearer may be sent to the mobile terminal 3 to display the position in a navigation software interface.

The data calculation means 21, 31, 41 respectively of the case 2, a smartphone 3 and a remote server 4 may indifferently and according to the applications carry out all or part of the steps of the method.

They each comprise to this end storage means in which are memorised all or part of sequences of code instructions for the execution of the method.

Prediction and Resetting

The calculation means implement (FIG. 3) a filtering 100 calculating on the one hand an estimation of the heading value by prediction (step 101) and on the other hand implementing a resetting as a function of an error estimation (step 102).

Notably, knowing the angular velocity ω given for example by a gyrometer, step 101 calculates the heading ψ_(k+1) at a time k+1 as equal to

ψ_(k+1)=ψ_(k) +ω·Δt

-   -   where ψ_(k) is the heading at the preceding time k and where Δt         is the duration separating these two sampling times.

The resetting 102 takes into account the measurements made by the magnetometers 20.

Hereafter, the measurement of the magnetic heading (derived from the measurements of the magnetometers) for a given time k is noted z_(ψ)[k], with

z _(ψ) [k]=ψ _(k)

Typically, the magnetic heading is given by

${z_{\psi}\lbrack k\rbrack} = {{atan}\left( \frac{{My}\lbrack k\rbrack}{{Mx}\lbrack k\rbrack} \right)}$

-   -   where My and Mx are two horizontal components of the magnetic         field in a terrestrial reference frame, these two components         being calculated as a function of the attitude determined for         the object 1 by an inertial unit thereof.

The calculation means calculate the reset heading ψ_(k+1) ^(reset) corresponding to time k+1 as equal to the sum of the estimated heading ψ_(k+1) at this time and a resetting which is advantageously a function

-   -   of a gain K_(k) calculated or adjusted with respect to the         preceding time k     -   of an estimation of the error Err(_(ψ) _(k+1) ,z_(ψ)) between         the predicted heading ψ_(k+1) and the measurement z_(ψ)

Thus, the calculation means use the magnetic heading derived from the measurement by the magnetometers to reset the state, and in particular the heading, by calculating

ψ_(k+1) ^(reset)=ψ_(k+1) +K _(k) ·Err(ψ_(k+1) ,z _(ψ))

Typically, the error Err(ψ_(k+1),z_(ψ)) may be a simple difference between the predicted heading, estimated at the time k+1 (before resetting), and the magnetic heading z_(ψ) derived from the magnetometer measurements.

Other error functions are nevertheless possible, notably in the case of a non-linear filtering.

In particular, the resetting K_(k)·Err(ψ_(k+1),z_(ψ)), and more particularly the gain K_(k), may advantageously depend on the magnetic field gradient measured by the magnetometers 20.

In this way, the resetting correction is all the greater when the magnetic field varies strongly and is thus liable to induce important errors on the heading measurement.

The reset heading value thereby obtained is stored by said calculation means 21, 31, 41 and/or used by said means for the remainder of the processing and for the calculations of magneto-inertial navigation information (linear velocity, angular velocity, position, heading, etc.).

Also, it may be transmitted by the calculation means to interface means, for example on the telephone to be displayed on the screen thereof.

Model of Change in Disturbances Linked to the Environment

An example of possible calculation of the resetting in which the measurement of magnetic heading z_(ψ) is corrected by an estimation of the disturbance of the magnetic field linked to the environment is detailed hereafter.

The magnetic heading z_(ψ) derived from the measurement by the magnetometers may in fact be considered as being broken down as follows:

z _(ψ)=ψ+ψ^((d)) +v _(z) _(ψ)

-   -   where:     -   ψ corresponds to the real heading that it is wished to         determine,     -   v_(z) _(ψ) corresponds to a Gaussian measurement error and     -   ψ^((d)) (“d” for disturbance) corresponds to a magnetic heading         disturbance linked to the environment (typically, disturbances         linked to metal infrastructures and to electric cables in urban         environments or in buildings).

The magnetic heading disturbance linked to the environment is highly correlated spatially. The magnetic field linked to disturbances of the environment is in fact a continuous vector field and the magnetic fields at two given points A and B are all the closer when these two points A and B are neighbouring in space.

In an embodiment, the heading disturbance ψ^((d)) linked to the environment is estimated by the calculation means by means of a formulation taking into account the change correlations that may be expected for the magnetic field disturbances between two successive sampling times (temporal, spatial correlation or more complex).

This estimation is constructed to enable a Markovian model (which may be used in a recursive filter) for the change in ψ_(d) and

-   -   makes it possible to take into account a model of the change in         the magnetic heading disturbance (temporal, spatial correlation         or more complex),     -   makes it possible to construct a filtering model for which the         heading is observable (otherwise, any hope of constructing a         heading estimator is lost).

In the proposed estimation, the amplitude of the resetting is estimated as a function of a model of the change in magnetic disturbances between two sampling times and an a priori estimation of the amplitude of the disturbances.

The Inventors have found (and mathematically verified) that in the case of a spatial correlation (case of disturbances in urban areas or indoors), a suitable estimation of the change in the disturbance ψ^((d)) between two sampling times separated by a time step is advantageously as follows:

${\psi^{(d)}\left\lbrack {k + 1} \right\rbrack} = {{{\alpha \lbrack k\rbrack}\left( {{\psi^{(d)}\lbrack k\rbrack} + {\hat{u}\lbrack k\rbrack}} \right)} + {\left( {1 - {\alpha \lbrack k\rbrack}} \right)\frac{\hat{u}\lbrack k\rbrack}{2}} + {v_{\psi^{(d)}}\lbrack k\rbrack}}$ where ${\alpha \lbrack k\rbrack} = {1 - \frac{{\sigma_{u}\lbrack k\rbrack}^{2}}{2{a\lbrack k\rbrack}^{2}}}$

-   -   a[k] being a parameter which represents the a priori amplitude         of the magnetic disturbance,     -   û and σ_(u) being the expectation and the variance in a random         variable which is a model (in the form of a random Gaussian         variable) of the variation in the magnetic heading disturbance         between 2 sampling times,     -   v_(ψ) _((d)) is an estimation taking into account the noise of         the magnetometers.

This estimation is subtracted from z_(ψ) for the error calculation, this being able to be directly calculated between ψ_(k+1) and (z_(ψ)−ψ^((d))[k+1]), or confined to a Kalman type filter which has both ψ^((d)) and ψ in its state.

Determination of the Parameter a[k]

The parameter a[k] represents the a priori amplitude of the magnetic heading disturbance. It characterises the heading and is for example calculated as a linear function of the norm of the magnetic field gradient.

For example,

a[k]=a ₀ +a ₁ N[k]

with

N[k]=∥

[k]∥

a₀ and a₁ being two parameters fixed beforehand before implementation of the filtering processing, {circumflex over (B)}[k] as long as the magnetic field is at time k.

In this way, as indicated above, the resetting term K_(k)·Err(ψ_(k+1),z_(ψ)) is a function of the magnetic field gradient measured by the magnetometers 20, which enables an efficient correction.

Other methods are possible to determine the parameter a[k].

Notably, a[k] may also be determined by comparison with a model of the Earth's magnetic field, for example by implementing the techniques such as proposed in the publication:

“Assessment of Indoor Magnetic Field Anomalies using Multiple Magnetometers Assessment of Indoor”—M. H. Afzal, V. Renaudin, G. Lachapelle—Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010) Sep. 21-24, 2010.

The solutions in which the parameter a[k] is a function of the magnetic field gradient enable however better corrections, and do not require models of the Earth's magnetic field.

Determination of the Parameter

The parameter û[k] represents the most probable value for the change in the disturbance.

This parameter is for example calculated using gyrometers that are assumed correct in the short term. The most probable change in the disturbance is then given by the difference between the change in the magnetic heading measurement and the change in the gyrometric heading:

$\begin{matrix} {{\hat{u}\lbrack k\rbrack} =} & {{E\left\lbrack {{\psi^{(d)}\left\lbrack {k + 1} \right\rbrack} - {\psi^{(d)}\lbrack k\rbrack}} \right\rbrack}} \\ {=} & {{E\left\lbrack {\underset{\underset{{{magnetic}\mspace{14mu} {heading}\mspace{14mu} {measured}\mspace{14mu} {at}\mspace{14mu} {timek}} + 1}{}}{{\psi^{(d)}\left\lbrack {k + 1} \right\rbrack} + {\psi \left\lbrack {k + 1} \right\rbrack}} -} \right.}} \\  & {\underset{{magnetic}\mspace{14mu} {heading}\mspace{14mu} {measured}\mspace{14mu} {at}\mspace{14mu} {timek}}{\left( \underset{}{{\psi^{(d)}\lbrack k\rbrack} + {\psi \lbrack k\rbrack}} \right) -}} \\  & \left. \underset{\underset{{change}\mspace{14mu} {in}\mspace{14mu} {heading}}{}}{\left( {{\psi \left\lbrack {k + 1} \right\rbrack} - {\psi \lbrack k\rbrack}} \right)} \right\rbrack \\ {=} & {{{z_{\psi}\left\lbrack {k + 1} \right\rbrack} - {z_{\psi}\lbrack k\rbrack} - {{\omega \lbrack k\rbrack}{dt}}}} \end{matrix}$

where: E[·] is the mathematical expectation, ω[k] is the gyrometric rotation velocity and dt is the sampling pitch.

Thus, the parameter û[k] is calculated by the calculation means as the difference between the magnetic headings determined directly from the magnetometer outputs for the times k+1 and k, from which is subtracted the predicted rotation ω[k]dt.

Determination of the Parameter σ_(u)

The parameter σ_(u) represents the image of the correlation between the disturbance at step k and that at step k+1.

It is possible to choose advantageously to index it on the velocity of displacement (or on the displacement between two successive sampling times, which is similar) in such a way as to take account of the spatial correlation of the magnetic disturbances.

One could for example take

σ_(u) =c·∥v∥

-   -   where c is an adjustment coefficient. 

1. Method for determining heading by magnetic sensors, in which a magnetic field is measured by magnetometers and calculation means implement a recursive processing calculating for a given sampling time: an estimation of a heading prediction which is a function of the heading determined at the preceding sampling time, a resetting of the predicted heading thereby estimated as a function of a magnetic heading determined from magnetometer measurements, characterised in that during said resetting, the calculation means estimate the amplitude of the resetting as a function: of a model of the change in magnetic disturbances between two sampling times determined beforehand to take into account a spatial correlation of the changes in disturbances, and of an a priori estimation of the amplitude of the disturbances.
 2. Method according to claim 1, in which for a given sampling time k+1, the calculation means estimate the heading disturbance linked to the environment by calculating ${{{\alpha \lbrack k\rbrack}\left( {{\psi^{(d)}\lbrack k\rbrack} + {\hat{u}\lbrack k\rbrack}} \right)} + {\left( {1 - {\alpha \lbrack k\rbrack}} \right)\frac{\hat{u}\lbrack k\rbrack}{2}} + {{v_{\psi^{(d)}}\lbrack k\rbrack}{where}{\alpha \lbrack k\rbrack}}} = {1 - \frac{{\sigma_{u}\lbrack k\rbrack}^{2}}{2{a\lbrack k\rbrack}^{2}}}$ and v_(ψ) _((d)) is a random Gaussian variable of variance a [k]²(1−α[k]²), k being the preceding sampling time, α[k] being a parameter which represents the a priori amplitude of the magnetic disturbance, û and σ_(u) being two parameters calculated by the calculation means as an estimation of the expectation and the variance in the change in disturbance.
 3. Method according to one of the preceding claims, in which said resetting is a function of the measured magnetic field gradient.
 4. Method according to claim 2 and claim 3, in which the calculation means estimate the parameter α[k] as a linear function of the norm of the magnetic field gradient.
 5. Method according to claim 2, in which the parameter û[k] is calculated by the calculation means as the difference between the magnetic headings determined directly from the magnetometer outputs for the times k+1 and k, from which is subtracted the predicted change in heading (ω[k]dt).
 6. Method according to claim 2, in which the parameter σ_(u) is estimated as a function of the velocity of displacement or the displacement between two successive sampling times.
 7. Method according to claim 2, in which the processing implements a Kalman filtering of which the state has at least as parameter the real heading and the magnetic heading disturbance (ψ, ψ^((d))).
 8. Method according to one of the preceding claims, in which the heading prediction is determined as a function of measurements of one or more sensors of an inertial unit.
 9. Method according to claim 1, in which the change model is determined beforehand in order to take account of a temporal correlation of the changes in disturbances.
 10. Device for determining heading by magnetic sensors, comprising magnetometers and calculation means for the calculation of the heading from the magnetic field measured by said magnetometers, characterised in that the calculation means implement, for different successive sampling times, the processing of the method according to one of the preceding claims.
 11. Magneto-inertial navigation system comprising at least one device for determining heading according to claim
 10. 12. Use of a system according to claim 11 in applications in urban environment or inside buildings.
 13. Computer programme product including code instructions for the execution of a magnetic field measurement method according to one of claims 1 to 9, when said programme is executed on a computer.
 14. Storage means readable by a computer equipment on which a computer programme product includes code instructions for the execution of a magnetic field measurement method according to one of claims 1 to
 9. 